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Question Bank No: 1

1. The odds in favour of throwing at least 8 in a single throw with two dice, are

a)		5 to 7
b)		5 to 36
c)		7 to 5
d)		None of these

2. The probability of scoring a total of 7 points at least one in two tosses of a pair of fair dice, is

a)		11/36
b)		1/4
c)		5/18
d)		11/36

3. If 1000 samples of 10 bolts each were taken in problem (59), the number of samples in which we shall expect to find 2 or more defective bolts, is

a)		620
b)		624
c)		625
d)		655

4. The probability of getting exactly three 6’s in 5 tosses of a fair die, is

a)		65/3888
b)		71/3888
c)		125/3888
d)		None of these

5. The probability that ‘4’ turns up at least once in two tosses of a fair die, is

a)		1/3
b)		5/18
c)		11/36
d)		None of these

6. The digits 1, 2, 3, ......, 9 are arranged in a random order. The probability that 1, 2, 3 will appear as neighbours in the order mentioned, is

a)		1/72
b)		1/36
c)		3/72
d)		1/18

7. The probability that the fifth day of a randomly chosen month of a randomly chosen year will be Friday, is

a)		2/7
b)		1/7
c)		1/14
d)		None of these

8. Three coins are tossed. The probability that not more than two coins will fall with head upwards, is

a)		5/8
b)		7/8
c)		3/8
d)		None of these

9. A man and his wife appear for an intervies for two posts. The probability of the man’s selection is 1/5 and that of his wife’s selection is 1/7. The probability that at least one of them is selected, is

a)		9/35
b)		12/35
c)		2/7
d)		11/35

10. In a simultaneous toss of 4 coins, the probability of getting exactly three heads, is

a)		3/8
b)		1/4
c)		1/2
d)		5/8

11. In a throw of two coins, the probability of getting both heads or both tails, is

a)		1/4
b)		1/2
c)		3/4
d)		None of these

12. An urn contains 10 blue and 6 red balls. 3 balls are drawn from the urn. The probability tat at least two of the balls drawn will be red, is

a)		17/56
b)		12/95
c)		17/95
d)		None of these

13. Twenty five coins are tossed simultaneously. The probability that the fifth coin will fall with head upwards, is

a)		5/25
b)		5/225
c)		1/2
d)		None of these

14. A bag contains 5 black and 3 white balls. Two balls are drawn from the bag at random and without replacement. The probability of obtaining both whitr balls. Is

a)		5/28
b)		1/9
c)		3/28
d)		none of these

15. The probabilirty that a leap year selected at random will contian 53 Sundays, is

a)		3/7
b)		1/7
c)		0
d)		2/7

16. One cards is drawn at random form an ordinary deck of well-shuffed cards. The probabiltiy that the card drawn will be either spade or an ace is

a)		17/52
b)		17/26
c)		4/13
d)		None of these

17. A box contains 10 green, 20 red, 30 yellow and 40 orange marbles. One marble is drawn from the box at random. The probability that this marble will be neither green nor orange, is

a)		$\frac{7}{10}$
b)		$\frac{1}{2}$
c)		$\frac{3}{5}$
d)		None of these

18. There is an objective type question with 4 answer choices exactly one of which is correct. A student has not studied the topic on which the question has been set. The probability that the student guesses the correct answer is

a)		$\frac{1}{2}$
b)		$\frac{1}{4}$
c)		$\frac{1}{8}$
d)		None of these

19. The probability that a college student will graduate is 0.4. The probability that cut of two college students exactly one will gradugate, is

a)		0.16
b)		0.24
c)		0.36
d)		None of these

20. A family has 4 children. A child is selected at random from the family. Assuming that there are equal number of boys and girls in the family, the probability that the selected child is a girl, is

a)		1/6
b)		1/4
c)		2/3
d)		1/2

21. The problem that a number selected at random from the set of numbers(1,2,3...100) is a cube is

a)		$\frac{1}{25}$
b)		$\frac{2}{25}$
c)		$\frac{3}{25}$
d)		$\frac{4}{25}$

22. A problem in maths is given to 3 students whose chances of solving individually are $\frac{1}{2}, \frac{1}{3} and \frac{1}{2} .$ The probability that the problem will be solved at least one is

a)		$\frac{1}{4}$
b)		$\frac{1}{24}$
c)		$\frac{23}{24}$
d)		$\frac{3}{4}$

23. A die throw 4 times .Probability of getting at most two 6 is

a)		0.984
b)		0.802
c)		0.621
d)		0.721

24. The probability that a masks man will met a tarket is given as $\frac{1}{5} then the probability of at least on hit is 10 shot is$

a)		1- ${(\frac{4}{5})}^{10}$
b)		$\frac{1}{5^{10}}$
c)		1- $\frac{1}{5^{10}}$
d)		${(\frac{4}{5})}^{10}$

25. A man is known to speak truth 3 out of 4 times.He throws a die and reports that it is a six. The probability that is actually a six is

a)		$\frac{1}{3}$
b)		$\frac{3}{8}$
c)		$\frac{3}{7}$
d)		$\frac{1}{2}$

26. If the probability that A and B with die with in a year are P and q respectively, then the probability that only one of them will be alive at the end of the year is

a)		P+q
b)		P+q-2pq
c)		P+q-pq
d)		P+q=pq

27. You are given a box with 20 cards 10 of these have letter I printed on them the other ten have the letter T printed on them.If you pick up 3 cards of random and keep them in same order,the probability of making the word IIT is

a)		$\frac{9}{80}$
b)		$\frac{1}{8}$
c)		$\frac{4}{27}$
d)		$\frac{5}{38}$

28. Two cards are drawn successively with replacement from a pack of 52 cards.The probability of drawing two aces is

a)		$\frac{1}{13} \times \frac{1}{13}$
b)		$\frac{1}{13} \times \frac{1}{17}$
c)		$\frac{1}{52} \times \frac{1}{51}$
d)		$\frac{1}{13} \times \frac{4}{51}$

29. A card is drawn at ramdom from a well shuffled pack of 52 cards.The probability of getting heart or diamond is

a)		$\frac{3}{13}$
b)		$\frac{1}{26}$
c)		$\frac{1}{2}$
d)		1

30. If A and B are the two mutually exclusive events such that P(B)=2P(A) and A $\cup$ B =S then P(A) is equal to

a)		$\frac{1}{2}$
b)		$\frac{2}{3}$
c)		$\frac{1}{3}$
d)		$\frac{3}{4}$

31. In a box containing 100 bulbs,10 are defective.What is the probability that out of a sample of 5 bulbs ,none is defective.

a)		$10^{- 5}$
b)		${(\frac{1}{2})}^{5}$
c)		${(\frac{9}{10})}^{5}$
d)		$\frac{9}{10}$

32. Three persons work independently on a problems.If the respective probabilities that they will solve it are $\frac{1}{3}, \frac{1}{4} and \frac{1}{5}, then the probability that none can solve it is$

a)		$\frac{3}{5}$
b)		$\frac{2}{5}$
c)		$\frac{1}{3}$
d)		none of these

33. If P(A)= $\frac{1}{4} P (\bar{B}) = \frac{1}{2} and P (A \cup B) = \frac{5}{9} then P (\frac{A}{B) is}$

a)		$\frac{7}{12}$
b)		$\frac{7}{18}$
c)		$\frac{7}{9}$
d)		$\frac{7}{36}$

34. A purse contains 4 copper coins and 3 silver coins, the second purse contains 6 copper coins and 2 silver coins.A coin is taken out from any purse.The probability that it is a copper coin is

a)		$\frac{4}{7}$
b)		$\frac{37}{56}$
c)		$\frac{3}{7}$
d)		$\frac{3}{4}$

35. An urn contains 7 green and 5 yellow balls. Two balls drawn at a time.The probability that both balls are of the same colour is

a)		$\frac{1}{3}$
b)		$\frac{5}{33}$
c)		$\frac{7}{22}$
d)		$\frac{31}{66}$

36. If $A_{1} A_{2} ... A_{8} are independent events such that P (Ai) = \frac{1}{1^{0} + 1}, 1 \leq i \leq 8, then the probability that none of the events occur is$

a)		$\frac{2}{9}$
b)		$\frac{1}{3}$
c)		$\frac{1}{2}$
d)		$\frac{1}{9}$

37. If x denote the number of sixes in four consecutive throws of a die,then P(x=4)

a)		$\frac{1}{1296}$
b)		$\frac{4}{6}$
c)		1
d)		$\frac{1295}{1296}$

38. Three identical dice are rolled .The probability that the same number appear on each of them is

a)		$\frac{1}{6}$
b)		$\frac{1}{36}$
c)		$\frac{1}{18}$
d)		$\frac{3}{28}$

39. A single letter is selected at random from the word "PROBABILITY". The probability that it is a vowel is

a)		$\frac{3}{11}$
b)		$\frac{4}{11}$
c)		$\frac{2}{11}$
d)		0

40. The probability of having atleast one tail in 4 throws with a coin is

a)		$\frac{15}{16}$
b)		$\frac{1}{16}$
c)		$\frac{1}{14}$
d)		1

41. A die is thrown once,then the probability of getting a number greater than 3 is

a)		$\frac{1}{2}$
b)		$\frac{1}{16}$
c)		-1
d)		1

42. In a probability distribution of x the sum of the probability is always

a)		zero
b)		1
c)		-1
d)		any non-negative integor

43. If A and B are such that P(A) $> 0 and P (B) \neq 1 then P (\bar{A} \cap \bar{B})) is equal to$

a)		1-P( $\frac{A}{B)}$
b)		1-P $(\frac{\bar{A}}{B})$
c)		$\frac{1 - P (A \cup B)}{P (\bar{B)})}$
d)		$\frac{P (A)}{P (B)}$

44. Two events A and B have probabilities 0.25 and 0.50 resoectively.The probability that both A and B occur Simultaneously is 0.14 then the probability that neither A nor B occur is

a)		0.39
b)		0.25
c)		0.11
d)		none of these

45. The Probability of a sure event is

a)		1
b)		2
c)		$\frac{1}{2}$
d)		unlimited

46. A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is

a)		$\frac{8}{9}$
b)		$\frac{8}{729}$
c)		$\frac{8}{243}$
d)		$\frac{1}{729}$

47. One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is

a)		$\frac{1}{2}$
b)		$\frac{1}{3}$
c)		$\frac{2}{5}$
d)		$\frac{1}{5}$

48. Let $E^{c}$ denote the complement of an event E. Let E, F, G be pairwise independent events with $P (G) > 0 and P (E \cap F \cap G) = 0.$ Then $P {(E}^{c} \cap F^{c} / G)$ equals

a)		$P {(E}^{c}) + P (F^{c})$
b)		$P {(E}^{c}) - P (F^{c})$
c)		$P {(E}^{c}) - P (F)$
d)		$P (E) - P (F^{c})$

49. Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all three apply for the same house is

a)		$\frac{1}{9}$
b)		$\frac{2}{9}$
c)		$\frac{7}{9}$
d)		$\frac{8}{9}$

50. Let A and b be two events such that $P (\bar{A \cup B}) = \frac{1}{6}, P (A \cap B) = \frac{1}{4}$ and $P (\bar{A}) = \frac{1}{4}$ . Then events A and B are

a)		equally likely, but not independent
b)		equally likely and mutually exclusive
c)		mutually exclusive and independent
d)		independent but not equally likely.